LMFDB - Embedded newform 729.2.g.c.55.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.8
Character	$\chi$	$=$	729.55
Dual form			729.2.g.c.676.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03275 - 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(-0.0188451 - 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(-6.85740 + 2.49589i) q^{8} +O(q^{10})$	\(q+(1.03275 - 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(-0.0188451 - 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(-0.794122 - 0.289037i) q^{10} +(-1.05229 - 0.692099i) q^{11} +(3.90613 + 0.456561i) q^{13} +(-6.00244 + 8.06268i) q^{14} +(-0.548323 + 9.41435i) q^{16} +(-3.68665 + 3.09347i) q^{17} +(-3.47862 - 2.91891i) q^{19} +(-1.06731 + 1.13128i) q^{20} +(-2.74377 + 1.80460i) q^{22} +(-0.546542 + 0.129533i) q^{23} +(4.86186 - 0.568270i) q^{25} +(5.12716 - 8.88050i) q^{26} +(9.24954 + 16.0207i) q^{28} +(-1.27398 - 1.71125i) q^{29} +(-1.09026 + 3.64174i) q^{31} +(8.93090 + 4.48526i) q^{32} +(3.59895 + 12.0213i) q^{34} +(-0.216961 + 1.23045i) q^{35} +(-0.248079 - 1.40693i) q^{37} +(-10.5810 + 5.31397i) q^{38} +(0.936794 + 2.17173i) q^{40} +(-3.74004 - 8.67039i) q^{41} +(-3.23349 + 1.62392i) q^{43} +(1.04952 + 5.95211i) q^{44} +(-0.254317 + 1.44230i) q^{46} +(-1.09079 - 3.64349i) q^{47} +(7.02487 + 3.52802i) q^{49} +(3.66055 - 12.2271i) q^{50} +(-11.2696 - 15.1377i) q^{52} +(-3.57369 - 6.18982i) q^{53} +(-0.204104 + 0.353518i) q^{55} +(27.9416 - 3.26591i) q^{56} +(-5.41276 + 1.28285i) q^{58} +(-4.88395 + 3.21222i) q^{59} +(6.33580 - 6.71556i) q^{61} +(7.59304 + 6.37131i) q^{62} +(5.51392 - 4.62673i) q^{64} +(0.0741126 - 1.27246i) q^{65} +(0.128801 - 0.173010i) q^{67} +(22.9381 + 2.68108i) q^{68} +(2.72186 + 1.79020i) q^{70} +(-11.2063 - 4.07874i) q^{71} +(7.37938 - 2.68588i) q^{73} +(-3.62465 - 0.859058i) q^{74} +(1.26704 + 21.7542i) q^{76} +(3.33192 + 3.53163i) q^{77} +(3.30367 - 7.65876i) q^{79} +3.05642 q^{80} -24.6211 q^{82} +(0.262659 - 0.608912i) q^{83} +(1.07039 + 1.13455i) q^{85} +(0.548576 + 9.41868i) q^{86} +(8.94335 + 2.11961i) q^{88} +(1.56940 - 0.571214i) q^{89} +(-14.2463 - 5.18524i) q^{91} +(2.25194 + 1.48112i) q^{92} +(-9.84973 - 1.15127i) q^{94} +(-0.878882 + 1.18054i) q^{95} +(0.937298 - 16.0928i) q^{97} +(15.7017 - 13.1753i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.03275	−	2.39419i	0.730266	−	1.69295i	0.00932059	−	0.999957i	$-0.497033\pi$
$2$	1.03275	−	2.39419i	0.730266	−	1.69295i	0.720946	−	0.692991i	$-0.243708\pi$
$3$		0			0
$3$		0			0
$4$	−3.29308	−	3.49047i	−1.64654	−	1.74523i
$5$	−0.0188451	−	0.323558i	−0.00842779	−	0.144700i	−0.999897	−	0.0143579i	$-0.995430\pi$
$5$	−0.0188451	−	0.323558i	−0.00842779	−	0.144700i	0.991469	−	0.130342i	$-0.0416074\pi$
$6$		0			0
$7$	−3.75109	−	0.889024i	−1.41778	−	0.336020i	−0.550913	−	0.834563i	$-0.685720\pi$
$7$	−3.75109	−	0.889024i	−1.41778	−	0.336020i	−0.866865	+	0.498543i	$0.833869\pi$
$8$	−6.85740	+	2.49589i	−2.42446	+	0.882430i
$9$		0			0
$10$	−0.794122	−	0.289037i	−0.251123	−	0.0914014i
$11$	−1.05229	−	0.692099i	−0.317276	−	0.208676i	0.380874	−	0.924627i	$-0.375623\pi$
$11$	−1.05229	−	0.692099i	−0.317276	−	0.208676i	−0.698151	+	0.715951i	$0.745993\pi$
$12$		0			0
$13$	3.90613	+	0.456561i	1.08337	+	0.126627i	0.638991	−	0.769214i	$-0.279352\pi$
$13$	3.90613	+	0.456561i	1.08337	+	0.126627i	0.444374	+	0.895841i	$0.353426\pi$
$14$	−6.00244	+	8.06268i	−1.60422	+	2.15484i
$15$		0			0
$16$	−0.548323	+	9.41435i	−0.137081	+	2.35359i
$17$	−3.68665	+	3.09347i	−0.894145	+	0.750277i	−0.969037	−	0.246915i	$-0.920583\pi$
$17$	−3.68665	+	3.09347i	−0.894145	+	0.750277i	0.0748921	+	0.997192i	$0.476139\pi$
$18$		0			0
$19$	−3.47862	−	2.91891i	−0.798050	−	0.669644i	0.149673	−	0.988735i	$-0.452178\pi$
$19$	−3.47862	−	2.91891i	−0.798050	−	0.669644i	−0.947724	+	0.319092i	$0.896622\pi$
$20$	−1.06731	+	1.13128i	−0.238658	+	0.252962i
$21$		0			0
$22$	−2.74377	+	1.80460i	−0.584973	+	0.384743i
$23$	−0.546542	+	0.129533i	−0.113962	+	0.0270095i	−0.287201	−	0.957870i	$-0.592725\pi$
$23$	−0.546542	+	0.129533i	−0.113962	+	0.0270095i	0.173239	+	0.984880i	$0.444577\pi$
$24$		0			0
$25$	4.86186	−	0.568270i	0.972371	−	0.113654i
$26$	5.12716	−	8.88050i	1.00552	−	1.74161i
$27$		0			0
$28$	9.24954	+	16.0207i	1.74800	+	3.02762i
$29$	−1.27398	−	1.71125i	−0.236572	−	0.317771i	0.667944	−	0.744212i	$-0.267175\pi$
$29$	−1.27398	−	1.71125i	−0.236572	−	0.317771i	−0.904516	+	0.426441i	$0.859767\pi$
$30$		0			0
$31$	−1.09026	+	3.64174i	−0.195817	+	0.654075i	0.802530	+	0.596611i	$0.203487\pi$
$31$	−1.09026	+	3.64174i	−0.195817	+	0.654075i	−0.998348	+	0.0574639i	$0.981699\pi$
$32$	8.93090	+	4.48526i	1.57877	+	0.792890i
$33$		0			0
$34$	3.59895	+	12.0213i	0.617215	+	2.06164i
$35$	−0.216961	+	1.23045i	−0.0366732	+	0.207984i
$36$		0			0
$37$	−0.248079	−	1.40693i	−0.0407839	−	0.231297i	0.957602	−	0.288095i	$-0.0930220\pi$
$37$	−0.248079	−	1.40693i	−0.0407839	−	0.231297i	−0.998386	+	0.0567981i	$0.981911\pi$
$38$	−10.5810	+	5.31397i	−1.71646	+	0.862039i
$39$		0			0
$40$	0.936794	+	2.17173i	0.148120	+	0.343381i
$41$	−3.74004	−	8.67039i	−0.584096	−	1.35409i	−0.912317	−	0.409486i	$-0.865708\pi$
$41$	−3.74004	−	8.67039i	−0.584096	−	1.35409i	0.328221	−	0.944601i	$-0.393551\pi$
$42$		0			0
$43$	−3.23349	+	1.62392i	−0.493102	+	0.247645i	−0.677931	−	0.735126i	$-0.737123\pi$
$43$	−3.23349	+	1.62392i	−0.493102	+	0.247645i	0.184829	+	0.982771i	$0.440827\pi$
$44$	1.04952	+	5.95211i	0.158221	+	0.897314i
$45$		0			0
$46$	−0.254317	+	1.44230i	−0.0374969	+	0.212656i
$47$	−1.09079	−	3.64349i	−0.159108	−	0.531458i	0.840844	−	0.541278i	$-0.182059\pi$
$47$	−1.09079	−	3.64349i	−0.159108	−	0.531458i	−0.999952	+	0.00982012i	$0.996874\pi$
$48$		0			0
$49$	7.02487	+	3.52802i	1.00355	+	0.504003i
$50$	3.66055	−	12.2271i	0.517680	−	1.72917i
$51$		0			0
$52$	−11.2696	−	15.1377i	−1.56281	−	2.09922i
$53$	−3.57369	−	6.18982i	−0.490884	−	0.850237i	0.509061	−	0.860731i	$-0.329993\pi$
$53$	−3.57369	−	6.18982i	−0.490884	−	0.850237i	−0.999945	+	0.0104941i	$0.996660\pi$
$54$		0			0
$55$	−0.204104	+	0.353518i	−0.0275214	+	0.0476684i
$56$	27.9416	−	3.26591i	3.73386	−	0.436425i
$57$		0			0
$58$	−5.41276	+	1.28285i	−0.710731	+	0.168446i
$59$	−4.88395	+	3.21222i	−0.635836	+	0.418196i	−0.826089	−	0.563539i	$-0.809439\pi$
$59$	−4.88395	+	3.21222i	−0.635836	+	0.418196i	0.190254	+	0.981735i	$0.439069\pi$
$60$		0			0
$61$	6.33580	−	6.71556i	0.811216	−	0.859839i	−0.181113	−	0.983462i	$-0.557970\pi$
$61$	6.33580	−	6.71556i	0.811216	−	0.859839i	0.992329	+	0.123623i	$0.0394514\pi$
$62$	7.59304	+	6.37131i	0.964317	+	0.809158i
$63$		0			0
$64$	5.51392	−	4.62673i	0.689240	−	0.578341i
$65$	0.0741126	−	1.27246i	0.00919253	−	0.157830i
$66$		0			0
$67$	0.128801	−	0.173010i	0.0157355	−	0.0211365i	−0.794186	−	0.607675i	$-0.792102\pi$
$67$	0.128801	−	0.173010i	0.0157355	−	0.0211365i	0.809921	+	0.586539i	$0.199510\pi$
$68$	22.9381	+	2.68108i	2.78165	+	0.325129i
$69$		0			0
$70$	2.72186	+	1.79020i	0.325325	+	0.213969i
$71$	−11.2063	−	4.07874i	−1.32994	−	0.484058i	−0.423308	−	0.905986i	$-0.639131\pi$
$71$	−11.2063	−	4.07874i	−1.32994	−	0.484058i	−0.906629	+	0.421928i	$0.861354\pi$
$72$		0			0
$73$	7.37938	−	2.68588i	0.863691	−	0.314358i	0.128082	−	0.991764i	$-0.459118\pi$
$73$	7.37938	−	2.68588i	0.863691	−	0.314358i	0.735610	+	0.677406i	$0.236896\pi$
$74$	−3.62465	−	0.859058i	−0.421357	−	0.0998635i
$75$		0			0
$76$	1.26704	+	21.7542i	0.145339	+	2.49538i
$77$	3.33192	+	3.53163i	0.379708	+	0.402467i
$78$		0			0
$79$	3.30367	−	7.65876i	0.371691	−	0.861678i	−0.625017	−	0.780611i	$-0.714908\pi$
$79$	3.30367	−	7.65876i	0.371691	−	0.861678i	0.996709	−	0.0810667i	$-0.0258327\pi$
$80$	3.05642			0.341718
$81$		0			0
$82$	−24.6211			−2.71894
$83$	0.262659	−	0.608912i	0.0288306	−	0.0668367i	−0.903192	−	0.429236i	$-0.858783\pi$
$83$	0.262659	−	0.608912i	0.0288306	−	0.0668367i	0.932023	+	0.362399i	$0.118042\pi$
$84$		0			0
$85$	1.07039	+	1.13455i	0.116100	+	0.123059i
$86$	0.548576	+	9.41868i	0.0591545	+	1.01564i
$87$		0			0
$88$	8.94335	+	2.11961i	0.953364	+	0.225951i
$89$	1.56940	−	0.571214i	0.166356	−	0.0605486i	−0.257500	−	0.966278i	$-0.582899\pi$
$89$	1.56940	−	0.571214i	0.166356	−	0.0605486i	0.423856	+	0.905730i	$0.360676\pi$
$90$		0			0
$91$	−14.2463	−	5.18524i	−1.49342	−	0.543561i
$92$	2.25194	+	1.48112i	0.234781	+	0.154418i
$93$		0			0
$94$	−9.84973	−	1.15127i	−1.01592	−	0.118744i
$95$	−0.878882	+	1.18054i	−0.0901714	+	0.121121i
$96$		0			0
$97$	0.937298	−	16.0928i	0.0951682	−	1.63397i	−0.526133	−	0.850403i	$-0.676358\pi$
$97$	0.937298	−	16.0928i	0.0951682	−	1.63397i	0.621301	−	0.783572i	$-0.286605\pi$
$98$	15.7017	−	13.1753i	1.58611	−	1.33091i
$99$		0			0
$100$	−17.9940	−	15.0988i	−1.79940	−	1.50988i
$101$	−2.37235	+	2.51454i	−0.236057	+	0.250206i	−0.834563	−	0.550912i	$-0.814280\pi$
$101$	−2.37235	+	2.51454i	−0.236057	+	0.250206i	0.598506	+	0.801118i	$0.295761\pi$
$102$		0			0
$103$	5.19032	−	3.41373i	0.511417	−	0.336364i	−0.267431	−	0.963577i	$-0.586175\pi$
$103$	5.19032	−	3.41373i	0.511417	−	0.336364i	0.778848	+	0.627213i	$0.215804\pi$
$104$	−27.9254	+	6.61845i	−2.73831	+	0.648992i
$105$		0			0
$106$	−18.5103	+	2.16355i	−1.79788	+	0.210142i
$107$	−0.773565	+	1.33985i	−0.0747833	+	0.129529i	−0.900992	−	0.433836i	$-0.857160\pi$
$107$	−0.773565	+	1.33985i	−0.0747833	+	0.129529i	0.826209	+	0.563364i	$0.190493\pi$
$108$		0			0
$109$	6.28071	+	10.8785i	0.601583	+	1.04197i	0.992581	+	0.121581i	$0.0387965\pi$
$109$	6.28071	+	10.8785i	0.601583	+	1.04197i	−0.390998	+	0.920391i	$0.627870\pi$
$110$	0.635601	+	0.853760i	0.0606022	+	0.0814029i
$111$		0			0
$112$	10.4264	−	34.8266i	0.985201	−	3.29080i
$113$	17.4823	+	8.77994i	1.64460	+	0.825947i	0.998007	+	0.0631087i	$0.0201015\pi$
$113$	17.4823	+	8.77994i	1.64460	+	0.825947i	0.646589	+	0.762838i	$0.276195\pi$
$114$		0			0
$115$	0.0522110	+	0.174397i	0.00486871	+	0.0162626i
$116$	−1.77774	+	10.0821i	−0.165059	+	0.936097i
$117$		0			0
$118$	2.64676	+	15.0105i	0.243654	+	1.38183i
$119$	16.5791	−	8.32636i	1.51981	−	0.763276i
$120$		0			0
$121$	−3.72857	−	8.64381i	−0.338961	−	0.785800i
$122$	−9.53500	−	22.1046i	−0.863259	−	2.00126i
$123$		0			0
$124$	16.3017	−	8.18702i	1.46393	−	0.735216i
$125$	−0.556893	−	3.15830i	−0.0498100	−	0.282487i
$126$		0			0
$127$	0.0822160	−	0.466270i	0.00729549	−	0.0413748i	−0.980943	−	0.194297i	$-0.937757\pi$
$127$	0.0822160	−	0.466270i	0.00729549	−	0.0413748i	0.988238	+	0.152922i	$0.0488685\pi$
$128$	0.349827	+	1.16850i	0.0309206	+	0.103282i
$129$		0			0
$130$	−2.96998	−	1.49158i	−0.260484	−	0.130820i
$131$	2.00931	−	6.71155i	0.175554	−	0.586391i	−0.824243	−	0.566236i	$-0.808399\pi$
$131$	2.00931	−	6.71155i	0.175554	−	0.586391i	0.999797	−	0.0201544i	$-0.00641578\pi$
$132$		0			0
$133$	10.4536	+	14.0417i	0.906445	+	1.21757i
$134$	−0.281198	−	0.487050i	−0.0242918	−	0.0420747i
$135$		0			0
$136$	17.5599	−	30.4146i	1.50575	−	2.60803i
$137$	−19.7273	+	2.30579i	−1.68541	+	0.196997i	−0.904153	−	0.427208i	$-0.859497\pi$
$137$	−19.7273	+	2.30579i	−1.68541	+	0.196997i	−0.781261	+	0.624205i	$0.785423\pi$
$138$		0			0
$139$	15.0469	−	3.56618i	1.27626	−	0.302479i	0.464032	−	0.885818i	$-0.346402\pi$
$139$	15.0469	−	3.56618i	1.27626	−	0.302479i	0.812229	+	0.583339i	$0.198254\pi$
$140$	5.00931	−	3.29468i	0.423364	−	0.278451i
$141$		0			0
$142$	−21.3386	+	22.6176i	−1.79069	+	1.89802i
$143$	−3.79438	−	3.18386i	−0.317302	−	0.266248i
$144$		0			0
$145$	−0.529681	+	0.444455i	−0.0439876	+	0.0369100i
$146$	1.19058	−	20.4415i	0.0985332	−	1.69175i
$147$		0			0
$148$	−4.09388	+	5.49904i	−0.336515	+	0.452018i
$149$	−8.59010	−	1.00404i	−0.703728	−	0.0822541i	−0.243300	−	0.969951i	$-0.578230\pi$
$149$	−8.59010	−	1.00404i	−0.703728	−	0.0822541i	−0.460428	+	0.887697i	$0.652304\pi$
$150$		0			0
$151$	2.53151	+	1.66500i	0.206011	+	0.135496i	0.648322	−	0.761366i	$-0.275471\pi$
$151$	2.53151	+	1.66500i	0.206011	+	0.135496i	−0.442311	+	0.896862i	$0.645841\pi$
$152$	31.1396	+	11.3339i	2.52575	+	0.919299i
$153$		0			0
$154$	11.8965	−	4.32995i	0.958643	−	0.348918i
$155$	1.19886	+	0.284135i	0.0962947	+	0.0228223i
$156$		0			0
$157$	−0.540951	−	9.28776i	−0.0431726	−	0.741244i	−0.948548	−	0.316633i	$-0.897448\pi$
$157$	−0.540951	−	9.28776i	−0.0431726	−	0.741244i	0.905376	−	0.424612i	$-0.139589\pi$
$158$	−14.9247	−	15.8192i	−1.18734	−	1.25851i
$159$		0			0
$160$	1.28294	−	2.97419i	0.101425	−	0.235130i
$161$	2.16529			0.170648
$162$		0			0
$163$	2.41567			0.189210			0.0946048	−	0.995515i	$-0.469841\pi$
$163$	2.41567			0.189210			0.0946048	+	0.995515i	$0.469841\pi$
$164$	−17.9474	+	41.6068i	−1.40146	+	3.24894i
$165$		0			0
$166$	−1.18659	−	1.25771i	−0.0920971	−	0.0976173i
$167$	−0.0292845	−	0.502796i	−0.00226611	−	0.0389075i	0.996986	−	0.0775876i	$-0.0247217\pi$
$167$	−0.0292845	−	0.502796i	−0.00226611	−	0.0389075i	−0.999252	+	0.0386800i	$0.987685\pi$
$168$		0			0
$169$	2.39981	+	0.568765i	0.184601	+	0.0437512i
$170$	3.82178	−	1.39101i	0.293117	−	0.106686i
$171$		0			0
$172$	16.3164	+	5.93867i	1.24411	+	0.452820i
$173$	4.45986	+	2.93329i	0.339077	+	0.223014i	0.707615	−	0.706598i	$-0.249771\pi$
$173$	4.45986	+	2.93329i	0.339077	+	0.223014i	−0.368538	+	0.929613i	$0.620142\pi$
$174$		0			0
$175$	−18.7425	−	2.19068i	−1.41680	−	0.165600i
$176$	7.09265	−	9.52709i	0.534629	−	0.718131i
$177$		0			0
$178$	0.253205	−	4.34736i	0.0189785	−	0.325848i
$179$	−13.8827	+	11.6490i	−1.03764	+	0.870683i	−0.991740	−	0.128263i	$-0.959060\pi$
$179$	−13.8827	+	11.6490i	−1.03764	+	0.870683i	−0.0458999	+	0.998946i	$0.514616\pi$
$180$		0			0
$181$	8.98433	+	7.53875i	0.667800	+	0.560351i	0.912413	−	0.409270i	$-0.134217\pi$
$181$	8.98433	+	7.53875i	0.667800	+	0.560351i	−0.244613	+	0.969621i	$0.578661\pi$
$182$	−27.1274	+	28.7534i	−2.01082	+	2.13134i
$183$		0			0
$184$	3.42456	−	2.25237i	0.252462	−	0.166047i
$185$	−0.450547	+	0.106782i	−0.0331249	+	0.00785074i
$186$		0			0
$187$	6.02040	−	0.703684i	0.440255	−	0.0514585i
$188$	−9.12542	+	15.8057i	−0.665539	+	1.15275i
$189$		0			0
$190$	1.91878	+	3.32342i	0.139203	+	0.241106i
$191$	−11.8767	−	15.9532i	−0.859367	−	1.15433i	−0.986713	−	0.162472i	$-0.948053\pi$
$191$	−11.8767	−	15.9532i	−0.859367	−	1.15433i	0.127346	−	0.991858i	$-0.459354\pi$
$192$		0			0
$193$	−4.57679	+	15.2875i	−0.329444	+	1.10042i	0.619505	+	0.784993i	$0.287333\pi$
$193$	−4.57679	+	15.2875i	−0.329444	+	1.10042i	−0.948950	+	0.315428i	$0.897852\pi$
$194$	−37.5612	−	18.8639i	−2.69674	−	1.35435i
$195$		0			0
$196$	−10.8190	−	36.1381i	−0.772789	−	2.58130i
$197$	−1.15341	+	6.54129i	−0.0821768	+	0.466048i	0.915753	+	0.401741i	$0.131595\pi$
$197$	−1.15341	+	6.54129i	−0.0821768	+	0.466048i	−0.997930	+	0.0643070i	$0.979516\pi$
$198$		0			0
$199$	−0.983166	−	5.57581i	−0.0696948	−	0.395259i	−0.999621	−	0.0275137i	$-0.991241\pi$
$199$	−0.983166	−	5.57581i	−0.0696948	−	0.395259i	0.929927	−	0.367745i	$-0.119870\pi$
$200$	−31.9214	+	16.0315i	−2.25718	+	1.13360i
$201$		0			0
$202$	3.57024	+	8.27674i	0.251201	+	0.582350i
$203$	3.25746	+	7.55165i	0.228629	+	0.530022i
$204$		0			0
$205$	−2.73489	+	1.37351i	−0.191013	+	0.0959304i
$206$	−2.81279	−	15.9521i	−0.195977	−	1.11144i
$207$		0			0
$208$	−6.44004	+	36.5233i	−0.446537	+	2.53244i
$209$	1.64033	+	5.47908i	0.113464	+	0.378996i
$210$		0			0
$211$	13.6528	+	6.85671i	0.939899	+	0.472035i	0.851678	−	0.524066i	$-0.175585\pi$
$211$	13.6528	+	6.85671i	0.939899	+	0.472035i	0.0882216	+	0.996101i	$0.471882\pi$
$212$	−9.83687	+	32.8574i	−0.675599	+	2.25666i
$213$		0			0
$214$	2.40896	+	3.23580i	0.164673	+	0.221195i
$215$	0.586367	+	1.01562i	0.0399899	+	0.0692645i
$216$		0			0
$217$	7.32727	−	12.6912i	0.497408	−	0.861535i
$218$	32.5317	−	3.80241i	2.20332	−	0.257531i
$219$		0			0
$220$	1.90607	−	0.451748i	0.128508	−	0.0304568i
$221$	−15.8129	+	10.4003i	−1.06369	+	0.699601i
$222$		0			0
$223$	−13.9427	+	14.7784i	−0.933674	+	0.989637i	−0.999967	−	0.00816311i	$-0.997402\pi$
$223$	−13.9427	+	14.7784i	−0.933674	+	0.989637i	0.0662922	+	0.997800i	$0.478883\pi$
$224$	−29.5131	−	24.7644i	−1.97192	−	1.65464i
$225$		0			0
$226$	39.0757	−	32.7884i	2.59928	−	2.18105i
$227$	0.0586242	−	1.00654i	0.00389103	−	0.0668063i	−0.995804	−	0.0915154i	$-0.970829\pi$
$227$	0.0586242	−	1.00654i	0.00389103	−	0.0668063i	0.999695	+	0.0247091i	$0.00786595\pi$
$228$		0			0
$229$	−6.05300	+	8.13059i	−0.399994	+	0.537285i	−0.955796	−	0.294030i	$-0.905004\pi$
$229$	−6.05300	+	8.13059i	−0.399994	+	0.537285i	0.555803	+	0.831314i	$0.312411\pi$
$230$	0.471461	+	0.0551059i	0.0310872	+	0.00363357i
$231$		0			0
$232$	13.0073	+	8.55502i	0.853969	+	0.561664i
$233$	18.4171	+	6.70328i	1.20654	+	0.439146i	0.865504	−	0.500902i	$-0.166998\pi$
$233$	18.4171	+	6.70328i	1.20654	+	0.439146i	0.341040	+	0.940049i	$0.389221\pi$
$234$		0			0
$235$	−1.15832	+	0.421596i	−0.0755608	+	0.0275019i
$236$	27.2954	+	6.46913i	1.77678	+	0.421104i
$237$		0			0
$238$	−2.81273	−	48.2927i	−0.182322	−	3.13035i
$239$	19.5911	+	20.7654i	1.26725	+	1.34320i	0.912951	+	0.408068i	$0.133798\pi$
$239$	19.5911	+	20.7654i	1.26725	+	1.34320i	0.354295	+	0.935134i	$0.384721\pi$
$240$		0			0
$241$	−4.81958	+	11.1731i	−0.310457	+	0.719719i	−0.999990	−	0.00453476i	$-0.998557\pi$
$241$	−4.81958	+	11.1731i	−0.310457	+	0.719719i	0.689533	+	0.724254i	$0.257816\pi$
$242$	−24.5456			−1.57785
$243$		0			0
$244$	−44.3047			−2.83632
$245$	1.00914	−	2.33944i	0.0644713	−	0.149461i
$246$		0			0
$247$	−12.2553	−	12.9898i	−0.779785	−	0.826524i
$248$	−1.61299	−	27.6940i	−0.102425	−	1.75857i
$249$		0			0
$250$	−8.13670	−	1.92843i	−0.514610	−	0.121965i
$251$	4.11036	−	1.49605i	0.259444	−	0.0944298i	−0.209024	−	0.977911i	$-0.567029\pi$
$251$	4.11036	−	1.49605i	0.259444	−	0.0944298i	0.468467	+	0.883481i	$0.344806\pi$
$252$		0			0
$253$	0.664768	+	0.241956i	0.0417936	+	0.0152116i
$254$	−1.03143	−	0.678382i	−0.0647177	−	0.0425655i
$255$		0			0
$256$	17.4574	+	2.04048i	1.09109	+	0.127530i
$257$	15.4931	−	20.8108i	0.966432	−	1.29814i	0.0119333	−	0.999929i	$-0.496201\pi$
$257$	15.4931	−	20.8108i	0.966432	−	1.29814i	0.954499	−	0.298215i	$-0.0963912\pi$
$258$		0			0
$259$	−0.320225	+	5.49805i	−0.0198978	+	0.341632i
$260$	−4.68555	+	3.93164i	−0.290585	+	0.243830i
$261$		0			0
$262$	−13.9936	−	11.7420i	−0.864528	−	0.725425i
$263$	19.5406	−	20.7118i	1.20492	−	1.27714i	0.254182	−	0.967157i	$-0.418194\pi$
$263$	19.5406	−	20.7118i	1.20492	−	1.27714i	0.950741	−	0.309987i	$-0.100325\pi$
$264$		0			0
$265$	−1.93542	+	1.27294i	−0.118892	+	0.0781964i
$266$	44.4144	−	10.5264i	2.72322	−	0.645416i
$267$		0			0
$268$	−1.02804	+	0.120160i	−0.0627973	+	0.00733995i
$269$	14.0246	−	24.2913i	0.855093	−	1.48106i	−0.0214661	−	0.999770i	$-0.506833\pi$
$269$	14.0246	−	24.2913i	0.855093	−	1.48106i	0.876559	−	0.481295i	$-0.159833\pi$
$270$		0			0
$271$	5.55847	+	9.62755i	0.337653	+	0.584832i	0.983991	−	0.178219i	$-0.0570337\pi$
$271$	5.55847	+	9.62755i	0.337653	+	0.584832i	−0.646338	+	0.763051i	$0.723700\pi$
$272$	−27.1015	−	36.4037i	−1.64327	−	2.20730i
$273$		0			0
$274$	−14.8529	+	49.6121i	−0.897296	+	2.99718i
$275$	−5.50936	−	2.76691i	−0.332227	−	0.166851i
$276$		0			0
$277$	−3.13137	−	10.4595i	−0.188146	−	0.628450i	−0.999063	−	0.0432889i	$-0.986216\pi$
$277$	−3.13137	−	10.4595i	−0.188146	−	0.628450i	0.810917	−	0.585161i	$-0.198969\pi$
$278$	7.00161	−	39.7081i	0.419929	−	2.38153i
$279$		0			0
$280$	−1.58327	−	8.97919i	−0.0946187	−	0.536609i
$281$	−4.19170	+	2.10515i	−0.250056	+	0.125583i	−0.569413	−	0.822052i	$-0.692829\pi$
$281$	−4.19170	+	2.10515i	−0.250056	+	0.125583i	0.319357	+	0.947634i	$0.396533\pi$
$282$		0			0
$283$	−12.8119	−	29.7014i	−0.761590	−	1.76556i	−0.633414	−	0.773813i	$-0.718347\pi$
$283$	−12.8119	−	29.7014i	−0.761590	−	1.76556i	−0.128177	−	0.991751i	$-0.540912\pi$
$284$	22.6664	+	52.5467i	1.34500	+	3.11807i
$285$		0			0
$286$	−11.5414	+	5.79632i	−0.682459	+	0.342744i
$287$	6.32103	+	35.8484i	0.373119	+	2.11606i
$288$		0			0
$289$	1.06984	−	6.06738i	0.0629319	−	0.356905i
$290$	0.517080	+	1.72717i	0.0303640	+	0.101423i
$291$		0			0
$292$	−33.6759	−	16.9127i	−1.97073	−	0.989739i
$293$	−5.74127	+	19.1772i	−0.335409	+	1.12034i	0.609439	+	0.792833i	$0.291395\pi$
$293$	−5.74127	+	19.1772i	−0.335409	+	1.12034i	−0.944848	+	0.327510i	$0.893791\pi$
$294$		0			0
$295$	1.13138	+	1.51971i	0.0658714	+	0.0884807i
$296$	5.21271	+	9.02868i	0.302983	+	0.524781i
$297$		0			0
$298$	−11.2753	+	19.5294i	−0.653161	+	1.13131i
$299$	−2.19400	+	0.256442i	−0.126882	+	0.0148304i
$300$		0			0
$301$	13.5728	−	3.21681i	0.782323	−	0.185414i
$302$	6.60074	−	4.34137i	0.379830	−	0.249818i
$303$		0			0
$304$	29.3870	−	31.1484i	1.68546	−	1.78649i
$305$	−2.29227	−	1.92344i	−0.131255	−	0.110136i
$306$		0			0
$307$	−4.16550	+	3.49527i	−0.237738	+	0.199486i	−0.753871	−	0.657023i	$-0.771816\pi$
$307$	−4.16550	+	3.49527i	−0.237738	+	0.199486i	0.516133	+	0.856509i	$0.327371\pi$
$308$	1.35474	−	23.2599i	0.0771933	−	1.32536i
$309$		0			0
$310$	1.91840	−	2.57686i	0.108958	−	0.146356i
$311$	−10.9151	−	1.27580i	−0.618941	−	0.0723438i	−0.199157	−	0.979968i	$-0.563820\pi$
$311$	−10.9151	−	1.27580i	−0.618941	−	0.0723438i	−0.419784	+	0.907624i	$0.637894\pi$
$312$		0			0
$313$	−20.7180	−	13.6264i	−1.17105	−	0.770211i	−0.193538	−	0.981093i	$-0.561996\pi$
$313$	−20.7180	−	13.6264i	−1.17105	−	0.770211i	−0.977512	+	0.210882i	$0.932367\pi$
$314$	−22.7953	−	8.29683i	−1.28642	−	0.468217i
$315$		0			0
$316$	−37.6119	+	13.6896i	−2.11583	+	0.770100i
$317$	22.7525	+	5.39244i	1.27791	+	0.302870i	0.812882	−	0.582428i	$-0.197897\pi$
$317$	22.7525	+	5.39244i	1.27791	+	0.302870i	0.465025	+	0.885298i	$0.346045\pi$
$318$		0			0
$319$	0.156235	+	2.68244i	0.00874746	+	0.150188i
$320$	−1.60093	−	1.69688i	−0.0894945	−	0.0948586i
$321$		0			0
$322$	2.23620	−	5.18410i	0.124619	−	0.288899i
$323$	21.8540			1.21599
$324$		0			0
$325$	19.2505			1.06783
$326$	2.49479	−	5.78357i	0.138173	−	0.320322i
$327$		0			0
$328$	47.2873	+	50.1216i	2.61100	+	2.76750i
$329$	0.852496	+	14.6368i	0.0469996	+	0.806953i
$330$		0			0
$331$	−15.2535	−	3.61514i	−0.838406	−	0.198706i	−0.211086	−	0.977467i	$-0.567700\pi$
$331$	−15.2535	−	3.61514i	−0.838406	−	0.198706i	−0.627320	+	0.778761i	$0.715848\pi$
$332$	−2.99034	+	1.08840i	−0.164116	+	0.0597335i
$333$		0			0
$334$	−1.23403	−	0.449151i	−0.0675233	−	0.0245765i
$335$	−0.0584059	−	0.0384142i	−0.00319106	−	0.00209879i
$336$		0			0
$337$	9.56786	+	1.11832i	0.521195	+	0.0609189i	0.372623	−	0.927983i	$-0.378458\pi$
$337$	9.56786	+	1.11832i	0.521195	+	0.0609189i	0.148572	+	0.988902i	$0.452532\pi$
$338$	3.84014	−	5.15821i	0.208876	−	0.280569i
$339$		0			0
$340$	0.435214	−	7.47234i	0.0236028	−	0.405244i
$341$	3.66771	−	3.07758i	0.198618	−	0.166660i
$342$		0			0
$343$	−2.54270	−	2.13358i	−0.137293	−	0.115203i
$344$	18.1202	−	19.2063i	0.976975	−	1.03553i
$345$		0			0
$346$	11.6288	−	7.64838i	0.625168	−	0.411179i
$347$	20.8248	−	4.93558i	1.11794	−	0.264956i	0.370200	−	0.928952i	$-0.379289\pi$
$347$	20.8248	−	4.93558i	1.11794	−	0.264956i	0.747736	+	0.663996i	$0.231141\pi$
$348$		0			0
$349$	30.6431	−	3.58167i	1.64029	−	0.191722i	0.754661	−	0.656115i	$-0.227802\pi$
$349$	30.6431	−	3.58167i	1.64029	−	0.191722i	0.885629	+	0.464393i	$0.153728\pi$
$350$	−24.6012	+	42.6106i	−1.31499	+	2.27763i
$351$		0			0
$352$	−6.29361	−	10.9008i	−0.335450	−	0.581017i
$353$	12.0041	+	16.1243i	0.638915	+	0.858211i	0.997152	−	0.0754191i	$-0.0240295\pi$
$353$	12.0041	+	16.1243i	0.638915	+	0.858211i	−0.358237	+	0.933631i	$0.616622\pi$
$354$		0			0
$355$	−1.10853	+	3.70274i	−0.0588345	+	0.196521i
$356$	−7.16196	−	3.59687i	−0.379583	−	0.190634i
$357$		0			0
$358$	13.5524	+	45.2683i	0.716268	+	2.39250i
$359$	−2.90565	+	16.4788i	−0.153354	+	0.869715i	0.806921	+	0.590660i	$0.201132\pi$
$359$	−2.90565	+	16.4788i	−0.153354	+	0.869715i	−0.960275	+	0.279056i	$0.909979\pi$
$360$		0			0
$361$	0.281455	+	1.59621i	0.0148134	+	0.0840111i
$362$	27.3278	−	13.7245i	1.43632	−	0.721345i
$363$		0			0
$364$	28.8155	+	66.8018i	1.51034	+	3.50137i
$365$	−1.00810	−	2.33704i	−0.0527665	−	0.122326i
$366$		0			0
$367$	21.8093	−	10.9531i	1.13844	−	0.571745i	0.223246	−	0.974762i	$-0.428335\pi$
$367$	21.8093	−	10.9531i	1.13844	−	0.571745i	0.915193	+	0.403017i	$0.132038\pi$
$368$	−0.919785	−	5.21636i	−0.0479471	−	0.271922i
$369$		0			0
$370$	−0.209648	+	1.18897i	−0.0108991	+	0.0618118i
$371$	7.90234	+	26.3956i	0.410269	+	1.37039i
$372$		0			0
$373$	11.5800	+	5.81569i	0.599589	+	0.301125i	0.722585	−	0.691282i	$-0.242954\pi$
$373$	11.5800	+	5.81569i	0.599589	+	0.301125i	−0.122996	+	0.992407i	$0.539250\pi$
$374$	4.53283	−	15.1407i	0.234387	−	0.782908i
$375$		0			0
$376$	16.5737	+	22.2624i	0.854725	+	1.14809i
$377$	−4.19503	−	7.26601i	−0.216055	−	0.374219i
$378$		0			0
$379$	5.56867	−	9.64522i	0.286043	−	0.495442i	−0.686818	−	0.726829i	$-0.740993\pi$
$379$	5.56867	−	9.64522i	0.286043	−	0.495442i	0.972862	+	0.231387i	$0.0743265\pi$
$380$	7.01488	−	0.819921i	0.359856	−	0.0420611i
$381$		0			0
$382$	−50.4606	+	11.9594i	−2.58179	+	0.611895i
$383$	26.5219	−	17.4437i	1.35521	−	0.891333i	0.356136	−	0.934434i	$-0.384094\pi$
$383$	26.5219	−	17.4437i	1.35521	−	0.891333i	0.999071	+	0.0431010i	$0.0137237\pi$
$384$		0			0
$385$	1.07990	−	1.14462i	0.0550367	−	0.0583355i
$386$	31.8746	+	26.7459i	1.62237	+	1.36133i
$387$		0			0
$388$	−59.2579	+	49.7233i	−3.00836	+	2.52432i
$389$	−0.398874	+	6.84840i	−0.0202237	+	0.347228i	0.972984	+	0.230873i	$0.0741581\pi$
$389$	−0.398874	+	6.84840i	−0.0202237	+	0.347228i	−0.993208	+	0.116355i	$0.962879\pi$
$390$		0			0
$391$	1.61421	−	2.16825i	0.0816339	−	0.109653i
$392$	−56.9779	−	6.65976i	−2.87782	−	0.336369i
$393$		0			0
$394$	14.4699	+	9.51701i	0.728984	+	0.479460i
$395$	−2.54031	−	0.924598i	−0.127817	−	0.0465216i
$396$		0			0
$397$	3.49386	−	1.27166i	0.175352	−	0.0638229i	−0.252852	−	0.967505i	$-0.581369\pi$
$397$	3.49386	−	1.27166i	0.175352	−	0.0638229i	0.428204	+	0.903682i	$0.359146\pi$
$398$	−14.3649	−	3.40455i	−0.720048	−	0.170655i
$399$		0			0
$400$	2.68402	+	46.0828i	0.134201	+	2.30414i
$401$	−22.7501	−	24.1137i	−1.13609	−	1.20418i	−0.976160	−	0.217052i	$-0.930356\pi$
$401$	−22.7501	−	24.1137i	−1.13609	−	1.20418i	−0.159926	−	0.987129i	$-0.551126\pi$
$402$		0			0
$403$	−5.92139	+	13.7273i	−0.294965	+	0.683807i
$404$	16.5892			0.825346
$405$		0			0
$406$	21.4442			1.06426
$407$	−0.712682	+	1.65218i	−0.0353263	+	0.0818957i
$408$		0			0
$409$	−16.6863	−	17.6865i	−0.825087	−	0.874541i	0.168720	−	0.985664i	$-0.446037\pi$
$409$	−16.6863	−	17.6865i	−0.825087	−	0.874541i	−0.993807	+	0.111123i	$0.964555\pi$
$410$	0.463987	+	7.96635i	0.0229147	+	0.393430i
$411$		0			0
$412$	−29.0076	−	6.87494i	−1.42910	−	0.338704i
$413$	21.1759	−	7.70738i	1.04200	−	0.379255i
$414$		0			0
$415$	−0.201968	−	0.0735104i	−0.00991423	−	0.00360848i
$416$	32.8374	+	21.5975i	1.60999	+	1.05891i
$417$		0			0
$418$	14.8120	+	1.73128i	0.724479	+	0.0846794i
$419$	3.36853	−	4.52473i	0.164564	−	0.221047i	−0.712190	−	0.701986i	$-0.752297\pi$
$419$	3.36853	−	4.52473i	0.164564	−	0.221047i	0.876754	+	0.480939i	$0.159704\pi$
$420$		0			0
$421$	−1.89250	+	32.4930i	−0.0922348	+	1.58361i	0.561882	+	0.827218i	$0.310078\pi$
$421$	−1.89250	+	32.4930i	−0.0922348	+	1.58361i	−0.654117	+	0.756394i	$0.726959\pi$
$422$	30.5163	−	25.6062i	1.48551	−	1.24649i
$423$		0			0
$424$	39.9553	+	33.5265i	1.94040	+	1.62819i
$425$	−16.1661	+	17.1350i	−0.784169	+	0.831171i
$426$		0			0
$427$	−29.7364	+	19.5580i	−1.43905	+	0.946476i
$428$	7.22413	−	1.71215i	0.349191	−	0.0827599i
$429$		0			0
$430$	3.03715	−	0.354992i	0.146465	−	0.0171193i
$431$	−0.705902	+	1.22266i	−0.0340021	+	0.0588934i	−0.882526	−	0.470264i	$-0.844159\pi$
$431$	−0.705902	+	1.22266i	−0.0340021	+	0.0588934i	0.848524	+	0.529158i	$0.177492\pi$
$432$		0			0
$433$	−3.07047	−	5.31820i	−0.147557	−	0.255576i	0.782767	−	0.622315i	$-0.213808\pi$
$433$	−3.07047	−	5.31820i	−0.147557	−	0.255576i	−0.930324	+	0.366739i	$0.880474\pi$
$434$	−22.8179	−	30.6498i	−1.09529	−	1.47124i
$435$		0			0
$436$	17.2882	−	57.7465i	0.827953	−	2.76555i
$437$	2.27931	+	1.14471i	0.109034	+	0.0547590i
$438$		0			0
$439$	3.81709	+	12.7500i	0.182180	+	0.608523i	0.999478	+	0.0323082i	$0.0102858\pi$
$439$	3.81709	+	12.7500i	0.182180	+	0.608523i	−0.817298	+	0.576215i	$0.804529\pi$
$440$	0.517279	−	2.93364i	0.0246603	−	0.139856i
$441$		0			0
$442$	8.56950	+	48.6000i	0.407610	+	2.31167i
$443$	−3.90497	+	1.96115i	−0.185531	+	0.0931770i	−0.539140	−	0.842216i	$-0.681251\pi$
$443$	−3.90497	+	1.96115i	−0.185531	+	0.0931770i	0.353609	+	0.935393i	$0.384954\pi$
$444$		0			0
$445$	−0.214396	−	0.497027i	−0.0101634	−	0.0235613i
$446$	20.9830	+	48.6440i	0.993573	+	2.30336i
$447$		0			0
$448$	−24.7965	+	12.4533i	−1.17152	+	0.588361i
$449$	−5.92614	−	33.6088i	−0.279672	−	1.58610i	−0.723719	−	0.690095i	$-0.757569\pi$
$449$	−5.92614	−	33.6088i	−0.279672	−	1.58610i	0.444047	−	0.896003i	$-0.353542\pi$
$450$		0			0
$451$	−2.06518	+	11.7122i	−0.0972454	+	0.551506i
$452$	−26.9246	−	89.9344i	−1.26643	−	4.23016i
$453$		0			0
$454$	−2.34930	−	1.17986i	−0.110258	−	0.0553737i
$455$	−1.40925	+	4.70724i	−0.0660668	+	0.220679i
$456$		0			0
$457$	1.56049	+	2.09610i	0.0729966	+	0.0980515i	0.837122	−	0.547016i	$-0.184236\pi$
$457$	1.56049	+	2.09610i	0.0729966	+	0.0980515i	−0.764125	+	0.645068i	$0.776829\pi$
$458$	13.2149	+	22.8889i	0.617493	+	1.06953i
$459$		0			0
$460$	0.436791	−	0.756545i	0.0203655	−	0.0352741i
$461$	−5.83610	+	0.682142i	−0.271814	+	0.0317705i	−0.250908	−	0.968011i	$-0.580729\pi$
$461$	−5.83610	+	0.682142i	−0.271814	+	0.0317705i	−0.0209061	+	0.999781i	$0.506655\pi$
$462$		0			0
$463$	24.7970	−	5.87700i	1.15241	−	0.273127i	0.390374	−	0.920657i	$-0.372346\pi$
$463$	24.7970	−	5.87700i	1.15241	−	0.273127i	0.762040	+	0.647529i	$0.224198\pi$
$464$	16.8089	−	11.0554i	0.780331	−	0.513232i
$465$		0			0
$466$	35.0692	−	37.1712i	1.62455	−	1.72192i
$467$	−20.6922	−	17.3628i	−0.957522	−	0.803456i	0.0230263	−	0.999735i	$-0.492670\pi$
$467$	−20.6922	−	17.3628i	−0.957522	−	0.803456i	−0.980548	+	0.196279i	$0.937114\pi$
$468$		0			0
$469$	−0.636953	+	0.534467i	−0.0294118	+	0.0246794i
$470$	−0.186883	+	3.20865i	−0.00862026	+	0.148004i
$471$		0			0
$472$	25.4738	−	34.2173i	1.17253	−	1.57498i
$473$	4.52646	+	0.529068i	0.208127	+	0.0243266i
$474$		0			0
$475$	−18.5713	−	12.2145i	−0.852109	−	0.560441i
$476$	−83.6593	−	30.4495i	−3.83452	−	1.39565i
$477$		0			0
$478$	69.9491	−	25.4594i	3.19940	−	1.16449i
$479$	−25.3313	−	6.00363i	−1.15742	−	0.274313i	−0.393312	−	0.919405i	$-0.628671\pi$
$479$	−25.3313	−	6.00363i	−1.15742	−	0.274313i	−0.764105	+	0.645092i	$0.776819\pi$
$480$		0			0
$481$	−0.326681	−	5.60890i	−0.0148954	−	0.255744i
$482$	21.7730	+	23.0780i	0.991731	+	1.05117i
$483$		0			0
$484$	−17.8924	+	41.4792i	−0.813291	+	1.88542i
$485$	−5.22461			−0.237238
$486$		0			0
$487$	−7.41759			−0.336123			−0.168061	−	0.985777i	$-0.553751\pi$
$487$	−7.41759			−0.336123			−0.168061	+	0.985777i	$0.553751\pi$
$488$	−26.6858	+	61.8647i	−1.20801	+	2.80048i
$489$		0			0
$490$	−4.55888	−	4.83213i	−0.205949	−	0.218293i
$491$	0.974800	+	16.7367i	0.0439921	+	0.755315i	0.946114	+	0.323834i	$0.104972\pi$
$491$	0.974800	+	16.7367i	0.0439921	+	0.755315i	−0.902122	+	0.431481i	$0.857991\pi$
$492$		0			0
$493$	9.99042	+	2.36777i	0.449946	+	0.106639i
$494$	−43.7568	+	15.9262i	−1.96871	+	0.716553i
$495$		0			0
$496$	−33.6868	−	12.2610i	−1.51258	−	0.550534i
$497$	38.4095	+	25.2624i	1.72290	+	1.13317i
$498$		0			0
$499$	−18.1347	−	2.11964i	−0.811821	−	0.0948882i	−0.299955	−	0.953953i	$-0.596972\pi$
$499$	−18.1347	−	2.11964i	−0.811821	−	0.0948882i	−0.511866	+	0.859065i	$0.671046\pi$
$500$	−9.19003	+	12.3444i	−0.410991	+	0.552056i
$501$		0			0
$502$	0.663161	−	11.3860i	0.0295983	−	0.508184i
$503$	−20.5047	+	17.2055i	−0.914261	+	0.767156i	−0.972925	−	0.231121i	$-0.925761\pi$
$503$	−20.5047	+	17.2055i	−0.914261	+	0.767156i	0.0586635	+	0.998278i	$0.481316\pi$
$504$		0			0
$505$	0.858307	+	0.720205i	0.0381942	+	0.0320487i
$506$	1.26583	−	1.34170i	0.0562730	−	0.0596459i
$507$		0			0
$508$	−1.89824	+	1.24849i	−0.0842209	+	0.0553930i
$509$	−28.5748	+	6.77235i	−1.26656	+	0.300179i	−0.808369	−	0.588677i	$-0.799649\pi$
$509$	−28.5748	+	6.77235i	−1.26656	+	0.300179i	−0.458187	+	0.888856i	$0.651501\pi$
$510$		0			0
$511$	−30.0685	+	3.51451i	−1.33015	+	0.155473i
$512$	21.6947	−	37.5763i	0.958780	−	1.66066i
$513$		0			0
$514$	−33.8245	−	58.5858i	−1.49194	−	2.58411i
$515$	−1.20235	−	1.61504i	−0.0529819	−	0.0711670i
$516$		0			0
$517$	−1.37383	+	4.58893i	−0.0604212	+	0.201821i
$518$	12.8327	+	6.44481i	0.563835	+	0.283169i
$519$		0			0
$520$	2.66771	+	8.91077i	0.116987	+	0.390763i
$521$	−1.78086	+	10.0998i	−0.0780209	+	0.442479i	0.920625	+	0.390449i	$0.127680\pi$
$521$	−1.78086	+	10.0998i	−0.0780209	+	0.442479i	−0.998646	+	0.0520298i	$0.983431\pi$
$522$		0			0
$523$	−5.81644	−	32.9867i	−0.254335	−	1.44241i	−0.797774	−	0.602957i	$-0.793989\pi$
$523$	−5.81644	−	32.9867i	−0.254335	−	1.44241i	0.543439	−	0.839449i	$-0.317122\pi$
$524$	−30.0432	+	15.0883i	−1.31244	+	0.659134i
$525$		0			0
$526$	−29.4074	−	68.1740i	−1.28222	−	2.97253i
$527$	−7.24618	−	16.7985i	−0.315648	−	0.731755i
$528$		0			0
$529$	−20.2716	+	10.1808i	−0.881375	+	0.442643i
$530$	1.04886	+	5.94840i	0.0455597	+	0.258382i
$531$		0			0
$532$	14.5873	−	82.7284i	0.632438	−	3.58673i
$533$	−10.6505	−	35.5752i	−0.461325	−	1.54093i
$534$		0			0
$535$	0.448098	+	0.225043i	0.0193730	+	0.00972948i
$536$	−0.451426	+	1.50787i	−0.0194986	+	0.0651300i
$537$		0			0
$538$	−43.6740	−	58.6643i	−1.88292	−	2.52920i
$539$	−4.95043	−	8.57440i	−0.213230	−	0.369325i
$540$		0			0
$541$	−19.3141	+	33.4530i	−0.830377	+	1.43826i	0.0673627	+	0.997729i	$0.478542\pi$
$541$	−19.3141	+	33.4530i	−0.830377	+	1.43826i	−0.897740	+	0.440526i	$0.854792\pi$
$542$	28.7907	−	3.36515i	1.23667	−	0.144546i
$543$		0			0
$544$	−46.8002	+	11.0918i	−2.00654	+	0.475559i
$545$	3.40147	−	2.23718i	0.145703	−	0.0958304i
$546$		0			0
$547$	7.78178	−	8.24821i	0.332725	−	0.352668i	−0.539314	−	0.842105i	$-0.681316\pi$
$547$	7.78178	−	8.24821i	0.332725	−	0.352668i	0.872039	+	0.489437i	$0.162798\pi$
$548$	73.0118	+	61.2642i	3.11891	+	2.61708i
$549$		0			0
$550$	−12.3143	+	10.3329i	−0.525084	+	0.440598i
$551$	−0.563296	+	9.67142i	−0.0239972	+	0.412016i
$552$		0			0
$553$	−19.2012	+	25.7916i	−0.816517	+	1.09677i
$554$	−28.2759	−	3.30498i	−1.20133	−	0.140415i
$555$		0			0
$556$	−61.9983	−	40.7769i	−2.62931	−	1.72933i
$557$	11.1013	+	4.04055i	0.470377	+	0.171203i	0.566323	−	0.824183i	$-0.308365\pi$
$557$	11.1013	+	4.04055i	0.470377	+	0.171203i	−0.0959459	+	0.995387i	$0.530588\pi$
$558$		0			0
$559$	−13.3718	+	4.86695i	−0.565568	+	0.205850i
$560$	−11.4649	−	2.71723i	−0.484481	−	0.114824i
$561$		0			0
$562$	0.711141	+	12.2098i	0.0299977	+	0.515040i
$563$	−14.0789	−	14.9227i	−0.593354	−	0.628918i	0.359210	−	0.933257i	$-0.383046\pi$
$563$	−14.0789	−	14.9227i	−0.593354	−	0.628918i	−0.952564	+	0.304338i	$0.901565\pi$
$564$		0			0
$565$	2.51136	−	5.82200i	0.105654	−	0.244933i
$566$	−84.3423			−3.54517
$567$		0			0
$568$	87.0259			3.65152
$569$	−6.45233	+	14.9582i	−0.270496	+	0.627080i	−0.998274	−	0.0587332i	$-0.981294\pi$
$569$	−6.45233	+	14.9582i	−0.270496	+	0.627080i	0.727778	+	0.685813i	$0.240553\pi$
$570$		0			0
$571$	−13.8809	−	14.7129i	−0.580898	−	0.615716i	0.368562	−	0.929603i	$-0.379850\pi$
$571$	−13.8809	−	14.7129i	−0.580898	−	0.615716i	−0.949460	+	0.313887i	$0.898369\pi$
$572$	1.38205	+	23.7289i	0.0577864	+	0.992154i
$573$		0			0
$574$	92.3559	+	21.8887i	3.85486	+	0.913618i
$575$	−2.58360	+	0.940353i	−0.107744	+	0.0392154i
$576$		0			0
$577$	3.36027	+	1.22304i	0.139890	+	0.0509157i	0.411016	−	0.911628i	$-0.365174\pi$
$577$	3.36027	+	1.22304i	0.139890	+	0.0509157i	−0.271126	+	0.962544i	$0.587396\pi$
$578$	−13.4216	−	8.82751i	−0.558264	−	0.367176i
$579$		0			0
$580$	3.29564	+	0.385205i	0.136844	+	0.0159948i
$581$	−1.52659	+	2.05057i	−0.0633338	+	0.0850720i
$582$		0			0
$583$	−0.523422	+	8.98680i	−0.0216779	+	0.372195i
$584$	−43.8997	+	36.8362i	−1.81658	+	1.52429i
$585$		0			0
$586$	39.9845	+	33.5510i	1.65174	+	1.38598i
$587$	5.44859	−	5.77516i	0.224887	−	0.238367i	−0.605099	−	0.796150i	$-0.706867\pi$
$587$	5.44859	−	5.77516i	0.224887	−	0.238367i	0.829986	+	0.557784i	$0.188348\pi$
$588$		0			0
$589$	14.4225	−	9.48584i	0.594269	−	0.390857i
$590$	4.80690	−	1.13926i	0.197897	−	0.0469024i
$591$		0			0
$592$	13.3813	−	1.56405i	0.549969	−	0.0642821i
$593$	−13.0180	+	22.5478i	−0.534584	+	0.925926i	0.464599	+	0.885521i	$0.346198\pi$
$593$	−13.0180	+	22.5478i	−0.534584	+	0.925926i	−0.999183	+	0.0404055i	$0.987135\pi$
$594$		0			0
$595$	−3.00650	−	5.20740i	−0.123254	−	0.213483i
$596$	24.7834	+	33.2898i	1.01517	+	1.36360i
$597$		0			0
$598$	−1.65189	+	5.51770i	−0.0675509	+	0.225636i
$599$	16.8175	+	8.44609i	0.687146	+	0.345098i	0.757877	−	0.652398i	$-0.226237\pi$
$599$	16.8175	+	8.44609i	0.687146	+	0.345098i	−0.0707306	+	0.997495i	$0.522533\pi$
$600$		0			0
$601$	−2.30500	−	7.69924i	−0.0940230	−	0.314059i	0.898021	−	0.439953i	$-0.145005\pi$
$601$	−2.30500	−	7.69924i	−0.0940230	−	0.314059i	−0.992044	+	0.125895i	$0.959820\pi$
$602$	6.31568	−	35.8180i	0.257408	−	1.45983i
$603$		0			0
$604$	−2.52485	−	14.3191i	−0.102734	−	0.582636i
$605$	−2.72651	+	1.36930i	−0.110848	+	0.0556701i
$606$		0			0
$607$	7.68029	+	17.8049i	0.311734	+	0.722680i	0.999996	−	0.00278207i	$-0.000885561\pi$
$607$	7.68029	+	17.8049i	0.311734	+	0.722680i	−0.688263	+	0.725462i	$0.741626\pi$
$608$	−17.9751	−	41.6710i	−0.728987	−	1.68998i
$609$		0			0
$610$	−6.97244	+	3.50169i	−0.282306	+	0.141779i
$611$	−2.59729	−	14.7300i	−0.105075	−	0.595910i
$612$		0			0
$613$	−2.54229	+	14.4180i	−0.102682	+	0.582339i	0.889439	+	0.457054i	$0.151095\pi$
$613$	−2.54229	+	14.4180i	−0.102682	+	0.582339i	−0.992121	+	0.125284i	$0.960016\pi$
$614$	4.06641	+	13.5828i	0.164107	+	0.548156i
$615$		0			0
$616$	−31.6629	−	15.9017i	−1.27573	−	0.640698i
$617$	5.94031	−	19.8420i	0.239148	−	0.798809i	−0.751184	−	0.660092i	$-0.770517\pi$
$617$	5.94031	−	19.8420i	0.239148	−	0.798809i	0.990332	−	0.138717i	$-0.0442977\pi$
$618$		0			0
$619$	−15.4730	−	20.7838i	−0.621912	−	0.835373i	0.373836	−	0.927495i	$-0.378042\pi$
$619$	−15.4730	−	20.7838i	−0.621912	−	0.835373i	−0.995748	+	0.0921222i	$0.970635\pi$
$620$	−2.95618	−	5.12026i	−0.118723	−	0.205635i
$621$		0			0
$622$	−14.3271	+	24.8154i	−0.574466	+	0.995005i
$623$	−6.39477	+	0.747442i	−0.256201	+	0.0299456i
$624$		0			0
$625$	22.8037	−	5.40457i	0.912146	−	0.216183i
$626$	−54.0208	+	35.5300i	−2.15911	+	1.42007i
$627$		0			0
$628$	−30.6372	+	32.4736i	−1.22256	+	1.29584i
$629$	5.26686	+	4.41942i	0.210004	+	0.176214i
$630$		0			0
$631$	−13.6194	+	11.4280i	−0.542180	+	0.454943i	−0.872283	−	0.489002i	$-0.837361\pi$
$631$	−13.6194	+	11.4280i	−0.542180	+	0.454943i	0.330102	+	0.943945i	$0.392917\pi$
$632$	−3.53914	+	60.7648i	−0.140780	+	2.41709i
$633$		0			0
$634$	36.4082	−	48.9047i	1.44596	−	1.94225i
$635$	−0.152415	−	0.0178147i	−0.00604840	−	0.000706956i
$636$		0			0
$637$	25.8293	+	16.9882i	1.02339	+	0.673097i
$638$	6.58363	+	2.39625i	0.260648	+	0.0948683i
$639$		0			0
$640$	0.371486	−	0.135210i	0.0146843	−	0.00534464i
$641$	−4.60209	−	1.09071i	−0.181771	−	0.0430806i	0.138722	−	0.990331i	$-0.455701\pi$
$641$	−4.60209	−	1.09071i	−0.181771	−	0.0430806i	−0.320493	+	0.947251i	$0.603849\pi$
$642$		0			0
$643$	0.490195	+	8.41632i	0.0193314	+	0.331907i	0.994084	+	0.108618i	$0.0346425\pi$
$643$	0.490195	+	8.41632i	0.0193314	+	0.331907i	−0.974752	+	0.223289i	$0.928321\pi$
$644$	−7.13047	−	7.55785i	−0.280980	−	0.297821i
$645$		0			0
$646$	22.5698	−	52.3227i	0.887997	−	2.05861i
$647$	23.1964			0.911943			0.455971	−	0.889994i	$-0.349292\pi$
$647$	23.1964			0.911943			0.455971	+	0.889994i	$0.349292\pi$
$648$		0			0
$649$	7.36248			0.289003
$650$	19.8810	−	46.0893i	0.779797	−	1.80777i
$651$		0			0
$652$	−7.95500	−	8.43180i	−0.311542	−	0.330215i
$653$	−2.10012	−	36.0577i	−0.0821841	−	1.41105i	−0.747390	−	0.664386i	$-0.768693\pi$
$653$	−2.10012	−	36.0577i	−0.0821841	−	1.41105i	0.665206	−	0.746660i	$-0.268344\pi$
$654$		0			0
$655$	−2.20944	−	0.523647i	−0.0863300	−	0.0204606i
$656$	83.6768	−	30.4559i	3.26703	−	1.18910i
$657$		0			0
$658$	35.9237	+	13.0752i	1.40045	+	0.509722i
$659$	−25.3331	−	16.6619i	−0.986839	−	0.649054i	−0.0499756	−	0.998750i	$-0.515914\pi$
$659$	−25.3331	−	16.6619i	−0.986839	−	0.649054i	−0.936863	+	0.349696i	$0.886285\pi$
$660$		0			0
$661$	12.8043	+	1.49661i	0.498030	+	0.0582114i	0.361400	−	0.932411i	$-0.382299\pi$
$661$	12.8043	+	1.49661i	0.498030	+	0.0582114i	0.136630	+	0.990622i	$0.456373\pi$
$662$	−24.4084	+	32.7862i	−0.948659	+	1.27427i
$663$		0			0
$664$	−0.281381	+	4.83112i	−0.0109197	+	0.187484i
$665$	4.34629	−	3.64697i	0.168542	−	0.141424i
$666$		0			0
$667$	0.917946	+	0.770248i	0.0355430	+	0.0298241i
$668$	−1.65856	+	1.75797i	−0.0641715	+	0.0680178i
$669$		0			0
$670$	−0.152290	+	0.100163i	−0.00588346	+	0.00386962i
$671$	−11.3149	+	2.68168i	−0.436807	+	0.103525i
$672$		0			0
$673$	−6.41242	+	0.749505i	−0.247181	+	0.0288913i	−0.238781	−	0.971073i	$-0.576748\pi$
$673$	−6.41242	+	0.749505i	−0.247181	+	0.0288913i	−0.00839975	+	0.999965i	$0.502674\pi$
$674$	12.5587	−	21.7523i	0.483744	−	0.837869i
$675$		0			0
$676$	−5.91752	−	10.2494i	−0.227597	−	0.394209i
$677$	10.4833	+	14.0815i	0.402905	+	0.541196i	0.956554	−	0.291554i	$-0.0941724\pi$
$677$	10.4833	+	14.0815i	0.402905	+	0.541196i	−0.553649	+	0.832750i	$0.686765\pi$
$678$		0			0
$679$	−17.8228	+	59.5322i	−0.683975	+	2.28464i
$680$	−10.1718	−	5.10848i	−0.390072	−	0.195901i
$681$		0			0
$682$	−3.58046	−	11.9596i	−0.137103	−	0.457956i
$683$	3.16828	−	17.9682i	0.121231	−	0.687535i	−0.862244	−	0.506492i	$-0.830942\pi$
$683$	3.16828	−	17.9682i	0.121231	−	0.687535i	0.983475	−	0.181042i	$-0.0579471\pi$
$684$		0			0
$685$	1.11782	+	6.33946i	0.0427097	+	0.242218i
$686$	−7.73418	+	3.88425i	−0.295292	+	0.148301i
$687$		0			0
$688$	−13.5151	−	31.3316i	−0.515259	−	1.19451i
$689$	−11.1333	−	25.8098i	−0.424144	−	0.983276i
$690$		0			0
$691$	−36.4273	+	18.2945i	−1.38576	+	0.695954i	−0.976309	−	0.216379i	$-0.930575\pi$
$691$	−36.4273	+	18.2945i	−1.38576	+	0.695954i	−0.409449	+	0.912333i	$0.634279\pi$
$692$	−4.44812	−	25.2266i	−0.169092	−	0.958970i
$693$		0			0
$694$	9.69020	−	54.9559i	0.367835	−	2.08610i
$695$	−1.43743	−	4.80134i	−0.0545247	−	0.182125i
$696$		0			0
$697$	40.6098	+	20.3950i	1.53821	+	0.772516i
$698$	23.0716	−	77.0645i	0.873273	−	2.91693i
$699$		0			0
$700$	54.0740	+	72.6340i	2.04381	+	2.74531i
$701$	21.5739	+	37.3671i	0.814834	+	1.41133i	0.909447	+	0.415820i	$0.136505\pi$
$701$	21.5739	+	37.3671i	0.814834	+	1.41133i	−0.0946129	+	0.995514i	$0.530161\pi$
$702$		0			0
$703$	−3.24372	+	5.61828i	−0.122339	+	0.211897i
$704$	−9.00438	+	1.05246i	−0.339365	+	0.0396661i
$705$		0			0
$706$	51.0020	−	12.0877i	1.91949	−	0.454926i
$707$	11.1344	−	7.32319i	0.418751	−	0.275417i
$708$		0			0
$709$	6.46423	−	6.85169i	0.242769	−	0.257321i	−0.594520	−	0.804081i	$-0.702658\pi$
$709$	6.46423	−	6.85169i	0.242769	−	0.257321i	0.837289	+	0.546761i	$0.184139\pi$
$710$	7.72023	+	6.47804i	0.289735	+	0.243116i
$711$		0			0
$712$	−9.33630	+	7.83409i	−0.349893	+	0.293595i
$713$	0.124151	−	2.13159i	0.00464949	−	0.0798286i
$714$		0			0
$715$	−0.958659	+	1.28770i	−0.0358518	+	0.0481573i
$716$	86.3771	+	10.0960i	3.22806	+	0.377306i
$717$		0			0
$718$	36.4525	+	23.9752i	1.36039	+	0.894745i
$719$	20.4128	+	7.42965i	0.761268	+	0.277079i	0.693339	−	0.720611i	$-0.256139\pi$
$719$	20.4128	+	7.42965i	0.761268	+	0.277079i	0.0679289	+	0.997690i	$0.478361\pi$
$720$		0			0
$721$	−22.5042	+	8.19087i	−0.838101	+	0.305044i
$722$	4.11231	+	0.974635i	0.153044	+	0.0362721i
$723$		0			0
$724$	−3.27242	−	56.1852i	−0.121618	−	2.08811i
$725$	−7.16635	−	7.59589i	−0.266152	−	0.282104i
$726$		0			0
$727$	8.91954	−	20.6778i	0.330807	−	0.766898i	−0.668915	−	0.743339i	$-0.733241\pi$
$727$	8.91954	−	20.6778i	0.330807	−	0.766898i	0.999722	−	0.0235590i	$-0.00749975\pi$
$728$	110.635			4.10039
$729$		0			0
$730$	−6.63645			−0.245626
$731$	6.89720	−	15.9895i	0.255102	−	0.591394i
$732$		0			0
$733$	−18.7053	−	19.8264i	−0.690895	−	0.732306i	0.283046	−	0.959106i	$-0.408655\pi$
$733$	−18.7053	−	19.8264i	−0.690895	−	0.732306i	−0.973941	+	0.226801i	$0.927173\pi$
$734$	−3.70006	−	63.5275i	−0.136572	−	2.34484i
$735$		0			0
$736$	−5.46210	−	1.29454i	−0.201336	−	0.0477174i
$737$	−0.255275	+	0.0929125i	−0.00940318	+	0.00342248i
$738$		0			0
$739$	−29.4451	−	10.7172i	−1.08316	−	0.394237i	−0.262075	−	0.965048i	$-0.584407\pi$
$739$	−29.4451	−	10.7172i	−1.08316	−	0.394237i	−0.821082	+	0.570811i	$0.806629\pi$
$740$	1.85641	+	1.22098i	0.0682429	+	0.0448841i
$741$		0			0
$742$	71.3573	+	8.34048i	2.61961	+	0.306189i
$743$	−25.9930	+	34.9147i	−0.953592	+	1.28090i	0.00614072	+	0.999981i	$0.498045\pi$
$743$	−25.9930	+	34.9147i	−0.953592	+	1.28090i	−0.959733	+	0.280915i	$0.909362\pi$
$744$		0			0
$745$	−0.162983	+	2.79832i	−0.00597125	+	0.102522i
$746$	25.8831	−	21.7185i	0.947648	−	0.795171i
$747$		0			0
$748$	−22.2819	−	18.6967i	−0.814706	−	0.683620i
$749$	4.09287	−	4.33819i	0.149550	−	0.158514i
$750$		0			0
$751$	−42.8341	+	28.1724i	−1.56304	+	1.02803i	−0.587224	+	0.809425i	$0.699779\pi$
$751$	−42.8341	+	28.1724i	−1.56304	+	1.02803i	−0.975814	+	0.218601i	$0.929851\pi$
$752$	34.8992	−	8.27126i	1.27264	−	0.301622i
$753$		0			0
$754$	−21.7286	+	2.53971i	−0.791311	+	0.0924909i
$755$	0.491017	−	0.850466i	0.0178699	−	0.0309516i
$756$		0			0
$757$	−6.51051	−	11.2765i	−0.236629	−	0.409853i	0.723116	−	0.690727i	$-0.242709\pi$
$757$	−6.51051	−	11.2765i	−0.236629	−	0.409853i	−0.959745	+	0.280874i	$0.909376\pi$
$758$	−17.3414	−	23.2936i	−0.629869	−	0.846061i
$759$		0			0
$760$	3.08034	−	10.2890i	0.111736	−	0.373223i
$761$	−21.1840	−	10.6390i	−0.767918	−	0.385663i	0.0213023	−	0.999773i	$-0.493219\pi$
$761$	−21.1840	−	10.6390i	−0.767918	−	0.385663i	−0.789220	+	0.614110i	$0.789515\pi$
$762$		0			0
$763$	−13.8882	−	46.3900i	−0.502788	−	1.67943i
$764$	−16.5730	+	93.9902i	−0.599591	+	3.40045i
$765$		0			0
$766$	−14.3730	−	81.5136i	−0.519319	−	2.94520i
$767$	−20.5439	+	10.3175i	−0.741797	+	0.372545i
$768$		0			0
$769$	15.9106	+	36.8849i	0.573750	+	1.33010i	0.919985	+	0.391954i	$0.128201\pi$
$769$	15.9106	+	36.8849i	0.573750	+	1.33010i	−0.346235	+	0.938148i	$0.612540\pi$
$770$	−1.62518	−	3.76760i	−0.0585675	−	0.135775i
$771$		0			0
$772$	68.4323	−	34.3680i	2.46293	−	1.23693i
$773$	−0.721794	−	4.09350i	−0.0259611	−	0.147233i	0.969072	−	0.246779i	$-0.0793721\pi$
$773$	−0.721794	−	4.09350i	−0.0259611	−	0.147233i	−0.995033	+	0.0995459i	$0.968261\pi$
$774$		0			0
$775$	−3.23122	+	18.3252i	−0.116069	+	0.658259i
$776$	33.7384	+	112.694i	1.21114	+	4.04548i
$777$		0			0
$778$	15.9844	+	8.02768i	0.573069	+	0.287806i
$779$	−12.2979	+	41.0778i	−0.440618	+	1.47177i
$780$		0			0
$781$	8.96929	+	12.0478i	0.320946	+	0.431106i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03275 - 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(-0.0188451 - 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(-6.85740 + 2.49589i) q^{8} +O(q^{10})\)	\(q+(1.03275 - 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(-0.0188451 - 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(-0.794122 - 0.289037i) q^{10} +(-1.05229 - 0.692099i) q^{11} +(3.90613 + 0.456561i) q^{13} +(-6.00244 + 8.06268i) q^{14} +(-0.548323 + 9.41435i) q^{16} +(-3.68665 + 3.09347i) q^{17} +(-3.47862 - 2.91891i) q^{19} +(-1.06731 + 1.13128i) q^{20} +(-2.74377 + 1.80460i) q^{22} +(-0.546542 + 0.129533i) q^{23} +(4.86186 - 0.568270i) q^{25} +(5.12716 - 8.88050i) q^{26} +(9.24954 + 16.0207i) q^{28} +(-1.27398 - 1.71125i) q^{29} +(-1.09026 + 3.64174i) q^{31} +(8.93090 + 4.48526i) q^{32} +(3.59895 + 12.0213i) q^{34} +(-0.216961 + 1.23045i) q^{35} +(-0.248079 - 1.40693i) q^{37} +(-10.5810 + 5.31397i) q^{38} +(0.936794 + 2.17173i) q^{40} +(-3.74004 - 8.67039i) q^{41} +(-3.23349 + 1.62392i) q^{43} +(1.04952 + 5.95211i) q^{44} +(-0.254317 + 1.44230i) q^{46} +(-1.09079 - 3.64349i) q^{47} +(7.02487 + 3.52802i) q^{49} +(3.66055 - 12.2271i) q^{50} +(-11.2696 - 15.1377i) q^{52} +(-3.57369 - 6.18982i) q^{53} +(-0.204104 + 0.353518i) q^{55} +(27.9416 - 3.26591i) q^{56} +(-5.41276 + 1.28285i) q^{58} +(-4.88395 + 3.21222i) q^{59} +(6.33580 - 6.71556i) q^{61} +(7.59304 + 6.37131i) q^{62} +(5.51392 - 4.62673i) q^{64} +(0.0741126 - 1.27246i) q^{65} +(0.128801 - 0.173010i) q^{67} +(22.9381 + 2.68108i) q^{68} +(2.72186 + 1.79020i) q^{70} +(-11.2063 - 4.07874i) q^{71} +(7.37938 - 2.68588i) q^{73} +(-3.62465 - 0.859058i) q^{74} +(1.26704 + 21.7542i) q^{76} +(3.33192 + 3.53163i) q^{77} +(3.30367 - 7.65876i) q^{79} +3.05642 q^{80} -24.6211 q^{82} +(0.262659 - 0.608912i) q^{83} +(1.07039 + 1.13455i) q^{85} +(0.548576 + 9.41868i) q^{86} +(8.94335 + 2.11961i) q^{88} +(1.56940 - 0.571214i) q^{89} +(-14.2463 - 5.18524i) q^{91} +(2.25194 + 1.48112i) q^{92} +(-9.84973 - 1.15127i) q^{94} +(-0.878882 + 1.18054i) q^{95} +(0.937298 - 16.0928i) q^{97} +(15.7017 - 13.1753i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more